shape-shifting surfaces that retain their effectiveness as physical barriers while undergoing changes in shape. The shape changes include any motion that makes the surface more effective at performing its function, such as expansion, shrinkage, twisting, encircling, wiggling, swallowing or constricting. The shape-shifting surfaces include tiled arrays of polygonal cells, each cell including specifically-designed compliant flexures attached to specifically-shaped overlapping thin plates or shells. Applications for such surfaces include micro-scale cellular engineering and macro-scale biomedical applications, recreational uses, national security, and environmental protection.
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7. A shape-shifting surface, comprising:
a single polygonal cell;
said single polygonal cell including compliant flexures attached to flat structures that retain their effectiveness as physical barriers while undergoing changes in shape;
said changes in shape selected from a group of changes including expansion, shearing, shrinkage, twisting, vibrating, encircling, wiggling, swallowing or constricting.
1. A unit cell shape shifting surface, comprising:
a plurality of layers adjacent overlapping side members;
said side members including compliant flexures and flat plate segments;
said complaint flexures enabling substantially straight line motion;
said overlapping side members being joined at nodes and being pivotal about said nodes, and
said overlapping side members forming a contiguous line of sight barrier.
12. A shape-shifting surface, comprising:
a tiled array of polygonal cells;
each polygonal cell of said tiled array including compliant flexures attached to flat structures that retain their effectiveness as physical barriers while undergoing changes in shape;
said changes in shape selected from a group of changes including expansion, shearing, shrinkage, twisting, vibrating, encircling, wiggling, swallowing or constricting.
2. The shape shifting surface of
each side member of said overlapping side members including a first node positioned at a free end of said compliant flexure and a second node at one corner of said plate segment.
3. The shape shifting surface of
all edges of said shape shifting surface remaining substantially within the boundary of the structure during deformation of said shape shifting surface.
4. The shape shifting surface of
said shape shifting surface returning to its original shape when said externally applied force is released.
5. The shape shifting surface of
said shape shifting surface maintaining a contiguous line of sight barrier when deforming in response to application of an externally applied force.
6. The shape shifting surface of
said plate segments being thin curved shells components.
8. The shape-shifting surface of
said structures including overlapping thin plates.
9. The shape-shifting surface of
said structures including overlapping thin shells.
10. The shape-shifting surface of
said structures including an initial planar structure and a specific final shape.
11. The shape-shifting structure of
said spatial structure selected from a group of shapes including spheres and cuboctohedrons.
13. The shape-shifting surface of
said structures including overlapping thin plates.
14. The shape-shifting surface of
said structures including overlapping thin shells.
15. The shape-shifting surface of
said structures including an initial planar structure and a specific final shape such as a spatial structure.
16. The shape-shifting structure of
said spatial structure selected from a group of shapes including spheres and cuboctohedrons.
17. A shape-shifting surface as in
a spatial structure formed of compliant mechanisms.
18. The shape-shifting surface of
said spatial structure formed of a plurality of planar compliant mechanisms.
19. The shape-shifting surface of
said spatial structure formed of a plurality of non-planar compliant mechanisms.
21. The shape-shifting structure of
said truncated icosahedron having planar faces.
22. The shape-shifting structure of
said truncated icosahedron having spherical faces.
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This application is a continuation of prior filed international application Ser. No. PCT/US2011/044370, entitled Shape-Shifting Surfaces, filed Jul. 18, 2011, which is a continuation of and claims priority to provisional patent application No. 61/365,164, entitled Design for Integrity in Shape-Shifting Surfaces, filed Jul. 16, 2010 by the same inventor.
1. Field of the Invention
This invention relates, generally, to surfaces the shape of which can be changed in response to externally applied forces. More particularly, it relates to such surfaces that are dynamic and controllable.
2. Description of the Prior Art
A compliant mechanism is a flexible mechanism, known to the art, that transfers an input force or displacement from one point to another through elastic body deformation. These mechanisms are most commonly designed in two ways. One is using pseudo-rigid-body models, and the other is using topology optimization. Both approaches have utility. The design of the compliant portion of the unit cell components is accomplished through compliant mechanism synthesis.
There are three major approaches to the design and synthesis of compliant mechanisms kinematic approximation methods, computationally intense methods, and linear and higher-order expansions of the governing equations. This disclosure is based primarily upon kinematic approximation methods.
The kinematic approximation or Pseudo-Rigid-Body Model (PRBM) approach works by identifying similarities between compliant mechanisms and rigid-body mechanisms. It has proved effective in identifying numerous compliant analogues to ubiquitous planar rigid-body mechanisms such as four-bar and crank-slider mechanisms. The chief criticisms of this approach are that the models are approximate and have limited, albeit known, accuracy. Moreover, the identification between flexure geometries and rigid-body mechanisms has been limited to a small but versatile set of planar configurations.
Computationally intense approaches typically combine finite element analysis with optimization to calculate optimal geometries in response to load and motion specifications. This approach has been successful, but has also been criticized for producing results identical to those produced more quickly by the PRBM approach, or results that are not physically realizable. As a general rule, this approach is more capable and accurate than the PRBM approach, but also more time consuming.
The third approach, which relies on linear and higher-order expansions of the governing equations, is well-known in precision mechanisms research, and relies heavily on flexures that are small and undergo small, nearly linear, deflections. This approach uses flexures much smaller than the overall mechanism size so it is not generally applicable to millimeter-scale and smaller mechanisms. These techniques are important but do not have a direct bearing on the invention disclosed herein.
Systems for subdividing surfaces in the development of finite element algorithms using node definition and degrees of freedom are known. These same subdivisions schemes are applicable to the design of the novel shape-shifting surfaces disclosed hereinafter. The prior art includes techniques for node placement in a given shape. For example, In Finite Element models, the behavior between nodes is typically determined by interpolating functions. In the shape-shifting system disclosed hereinafter, a kinematic scheme is required to fill the gaps between nodes. Thus, kinematic skeletons are developed which have the same number of nodes (typically revolute joints) and the same number of degrees of freedom. Methods for enumerating all possible kinematic linkages with a given number of degrees of freedom are known. The simplest systems satisfying degree of freedom requirements are preferred. For example, triangular elements with additional nodes along the edges and center-point nodes are known.
Tiling systems, periodic and aperiodic, are methods for subdividing surfaces and as such have been extensively studied by mathematicians and artists since antiquity. The three regular tilings are: 1) equilateral triangles only, 2) squares only, and 3) regular hexagons only. There are eight Archimedian tilings, and there are aperiodic Penrose kite-and-dart tiling systems. The regular tilings are simple and require the fewest different types of unit cells. Some of the Archimedian tilings use polygons with several sides, yielding generous angles and areas to work with, which may be advantageous. Penrose tiles are specifically shaped quadrilaterals that can be assembled in multiple, non-periodic ways.
In 1827, Carl Fredrich Gauss published his ‘Theorema Egregium’ which is the foundational result in differential geometry. The basic result is that small triangles do not change their shape when bent and that there is a fundamental difference in the shape of triangles that are planar (the sum of the angles is equal to 180 degrees) and the shape of triangles on a sphere (the sum of the angles is always more than 180 degrees) and the shape of triangles on a hyperbolic or saddle-shaped surface (the sum of the angles is always less than 180 degrees). His result means that spheres cannot be made into planes without crumpling or tearing or stretching (distorting) the surface. This fundamental geometric limitation makes the building of certain types of curved surfaces (those with two non-zero principal curvatures) intrinsically more difficult than working with planar surfaces (both principal curvatures equal to zero) or developable surfaces (one principal curvature equal to zero).
This leads to a need for innovation that allows conventional surfaces to achieve new functionality, to be constructed more precisely, or at lower cost. More particularly, a low-cost modular building system with customizable degrees-of-freedom and stiffness is needed. In addition to potential savings when a new barrier is erected, an innovative system would provide new methods and functionality to surfaces and objects.
Objects that function as physical barriers or supporting surfaces include walls, table tops, shelves, floors, ceilings, stairs, vehicle bodies, and pipelines. Conventional methods for constructing these barriers can be costly, but even when they are inexpensive, the numbers of these kinds of objects mean that they represent a significant economic investment. Such barriers often incur additional costs when they require modification or removal. Thus there is a need for a surface, and a method for designing such surface, having a shape that may be modified or adjusted without damaging the surface or rebuilding it.
However, in view of the art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill how said art could be advanced.
The novel shape-shifting surfaces disclosed herein may include a single polygonal cell structure comprising multiple side members that have compliant flexures and plate or shell segments. The side members are attached at nodes to form structures that retain their effectiveness as physical line of sight barriers while undergoing changes in shape such as expansion, shearing, shrinkage, twisting, vibrating, encircling, wiggling, swallowing or constricting.
The single polygonal cell structures may include overlapping thin plates, overlapping thin shells, or both.
The novel shape-shifting surfaces may also be formed of a tiled array of polygonal cells including compliant flexures attached to structures that retain their effectiveness as physical barriers while undergoing changes in shape such as expansion, shearing, shrinkage, twisting, vibrating, encircling, wiggling, swallowing or constricting. Such structures, when joined to multiple other cell structures, may further include a specific final shape such as a sphere, cuboctohedron, or other spatial structures.
Said tiled array structures may further include an initial planar structure and a specific final shape such as a sphere, cuboctohedron, or other spatial structures formed of compliant mechanisms including planar and non-planar compliant mechanisms.
The novel shape-shifting structure may further include a truncated icosahedron having planar or spherical faces, or both.
The novel method of incorporating shape-shifting surfaces in existing design tools includes the step of modeling a shape-shifting system cell using a single finite element for each unit cell, with material properties that are a known modification of the material used to fabricate the compliant portion of the unit cell so that a well-characterized shape-shifting system relates the properties of a unit cell to the properties of a geometrically similar element of bulk material.
An important object of this invention is to disclose shape-shifting surfaces, i.e., surfaces that retain their effectiveness as a physical barrier while undergoing changes in shape and which maintain the relative integrity of a surface while changing the size of the area they cover.
There are different levels of barrier effectiveness such as line-of-sight (or radiation) barriers. Water-tight barriers and air-tight barriers may be achievable with the right choice of material, although it might be required to add layers that stretch, fold and perhaps crumple in order to accommodate the shape-changes.
Another object is to provide shape-shifting surfaces that provide changes in shape including expansion, shrinkage, twisting, encircling, swallowing, and constricting motions that make the surface more effective at performing its function.
Another object is to disclose compliant mechanisms that enable motion and provide a stable ‘default’ shape for a surface.
These and other important objects, advantages, and features of the invention will become clear as this disclosure proceeds.
The invention accordingly comprises the features of construction, combination of elements, and arrangement of parts that will be exemplified in the disclosure set forth hereinafter and the scope of the invention will be indicated in the claims.
For a fuller understanding of the nature and objects of the invention, reference should be made to the following detailed disclosure, taken in connection with the accompanying drawings, in which:
A shape-shifting surface, a coined term, is a novel flat or curved surface that can change its shape (including its area and the orientation of internal lines) while maintaining integrity against various forms of external assaults. Shape-shifting surfaces have potential utility in products as diverse as containers, shielding, furniture, architectural elements, clothing, exercise equipment, and children's toys.
Shape-shifting surfaces may also have applications in the fields of reconfigurable robotic systems such as claytronics, programmable matter, and digital clay. An important distinction is that shape-shifting surfaces are functional without any actuation. Shape-shifting surfaces include compliant mechanisms so a rich variety of passive behaviors can be designed into them without the inherent expense of large numbers of actuators and processors.
The novel shape-shifting surface concept disclosed herein offers the first plausible workaround to Guass's result: shape-shifting surfaces can change their area because they have multiple layers which can slide with respect to each other. Thus, it functions as an integral surface, and can satisfy many of the practical expectations that we have of surfaces, but because of the multiplicity of layers it provides functionality that is not seen in any other structure or mechanism. Thus, a spherical globe made of shape-shifting surfaces could potentially be opened and pressed flat into a flat map. The gaps (or tears) that would open in a conventional surface (e.g. typical cardboard or metal globes) would be filled by underlying layers being revealed as the surface was stretched flat. Because the stretching motions in a shape-shifting surface are controlled by elastic members, the stretching motions are reversible.
The passive functionality of a shape-shifting surface is a functionality that is designed in due to the geometry and material properties of the shape-shifting surface, and that does not require electronic sensors or actuators to achieve. As a new design paradigm, shape-shifting surfaces may be components in improved reconfigurable robotic systems.
This disclosure discloses three design concepts associated with shape-shifting surfaces: 1) Characterizing a shape-shifting surface unit cell as a finite element, thereby enhancing the feasibility of integrating the shape-shifting surface into existing designs and simplifying its analysis; 2) Establishing a kinematic and structural basis for shape-shifting, i.e., deforming the geometry of each cell, and using a rigid-body-replacement technique to identify compliant mechanisms with motions consistent with the kinematic structure; and 3) The integration of unit cells into complex polygonal surfaces and shapes such as a cube or cuboctahedron, as depicted in
Modeling the unit cell as a finite element requires consideration of design space characterization of the shape-shifting system, node definition and degrees of freedom, and periodic or aperiodic tiling systems. Concerning design space considerations, designers are more likely to use a design innovation if it can be easily integrated into existing software and design procedures. Accordingly, the design space allows shape-shifting system designs to be easily assessed using existing tools. This is achievable because a shape-shifting system cell can be modeled using a single finite element for each unit cell, with material properties that are a known modification of the material used to fabricate the compliant portion of the unit cell. Thus, a well-characterized shape-shifting system relates the properties of a unit cell to the properties of a geometrically similar element of bulk material. For example, an initial polypropylene cell prototype, designed for minimal stiffness, has one-fourth the density and 1/1500th the in-plane stiffness of a uniform block of polypropylene with equal area and thickness. The ratio between the properties of the shape-shifting system cell and the bulk material allows designers to test concepts in standard design software using modified material properties.
A shape-shifting surface has a specific initial shape but is made of a material that accommodates deformation of that shape in order to produce the desired shape-shifting property. There may be a specific initial shape, i.e., a planar arrangement such as an ellipse and a different specific final shape, i.e., a spatial figure such as a sphere or cuboctohedron as depicted in
Shape-shifting surfaces have multiple sub-components; accordingly, elastic members are necessary to give them a default shape. Without such elastic members, shape-shifting surfaces are too vulnerable to gravity and would collapse under their own weight.
Based on the properties of small triangular areas, mathematicians have recognized three basic categories of surfaces: hyperbolic surfaces, spherical surfaces and planar surfaces. Each type of surface can generally be subdivided into regular polygonal areas. Each of these regular polygons can be taken as a unit cell for the purposes of design. Systems of tiling for the three types of surfaces include regular, Archimedean, and Penrose tiling systems. Computer algorithms for generating these tiling systems are adapted for use in describing shape-shifting surfaces.
The design of shape shifting surfaces may be accomplished using the approach taken in finite element analysis where the vertices of the unit cells are taken as nodes. For example, a simple planar square unit cell has four nodes, each node with two translational degrees of freedom, yielding eight degrees of freedom for the unit cell.
Given the unit cell shape and its required degrees of freedom, kinematic skeleton models are constructed that result in the nodes having appropriate relative freedoms. A nodal model and a simple kinematic model, consisting of links, revolute joints and sliding joints, are depicted in
A polygon has a finite number of straight sides joined at corners which are known as the nodes of the unit cell. For example, a square has four corners, so a square unit cell has four nodes as depicted in
To define link shapes that preserve line-of-sight surface integrity, shapes are chosen for each of the links in the kinematic model so that as the links slide, rotate, and overlap, the unit cell serves, at the minimum, as a line-of-sight barrier for all points within the unit cell. At the same time, no piece of the links intrudes on adjacent unit cells, and the number of overlapping layers is minimized.
A graphical strategy permits designing link shapes with maximal motion range from the starting position. For the relative sliding motion of two squares, the minimum area of coverage occurs when they are coincident as depicted in
The length change of each side is accomplished by a design in which each side of the unit cell consists of two separate side members which can translate relative to each other as depicted in
Furthermore, the link shapes may be described as side members of a unit cell.
In deference to the stresses associated with moving compliant portions of the shape shifting surface, an intermediate design with half of each member overlapping the other member as depicted in
The sides can be subdivided further if desired. If X is the minimum width, and n is the number of side members, then the maximum width is nX. The midpoint length, Y, is found by averaging the minimum and maximum widths, Y=(X+nX)/2. Thus, if the unit cell width is equated to be the midpoint length, Y, then the length of each side member is given by X=2Y/(n+1). The range of motion for each side is then given by R=2Y(n−1)/n+1. This equation assumes a minimum of two members but it gives a correct result when n=1, i.e, with a single side member, the range of motion for a side becomes zero.
Rotations can be approached similarly.
Similar results can be obtained for the range of motion of a corner. A corner consisting of a single member is immobile, so two corner members, pinned at the corner can move with respect to each other. When two corner members are used, they can either osculate as shown in
For a corner that is originally ninety degrees (90°), the two-thirds rule suggests two members with sixty degree (60°) corners. Thus, the corner can expand to one hundred twenty degrees (120°), and compress to sixty degrees (60°).
These design rules disclose how to design sides and angles that can compress and expand without developing gaps or without protruding past the nodes. Following these rules produces shape shifting surface members that provide good coverage and a range of motion without gaps in the shape shifting surface or protrusions outside of the unit cell.
To identify compliant mechanisms with motions consistent with the kinematic structure, kinematic models consisting of sliders and revolute joints are simplified and made easier to assemble by replacing rigid-link mechanisms with a compliant mechanism having the same motion. This process is known as compliant mechanism synthesis by rigid-body replacement.
A compliant mechanism depicted in
Selecting a tiling scheme is one step of the design procedure for a shape shifting surface. The tiles may be of regular configuration such as equilateral triangles, squares, or regular hexagons. They may also be Archimedean or even non-periodic such as Penrose tiles. In general, the selected tiling scheme will include a finite number of polygonal shapes that are repeated to fill an area. The polygons used in the tiling schemes are used to design each of the unit cells of a shape-shifting surface.
Applying these design rules, suppose a square unit cell is chosen and that an application requires that each of the four sides and four corners must be able to expand and contract. The minimum number of side members for which this can be achieved is eight (8). Each side of the square unit cell is associated with two side members, and each corner is associated with two side members. The two-thirds rule is used to select the length of the side member and the angle of the member attached at the node (see
The remaining portion of the shape shifting surface, i.e., the portion of the side member depicted in
The black arrows in
There are a number of compliant mechanisms which can achieve the desired straight line motion. These can be designed using rigid-body replacement methodology. The fundamental principles include rigid-body mechanism techniques for straight-line mechanism design and rigid-body replacement methods to eliminate the need for joints and to give the mechanism stiffness or resistance to motion. The use of compliant members in the shape shifting surface design allows for motion with fewer parts and it provides a default or in repose shape to which the shape shifting surface tends to return when external forces are removed.
Eight side-members are assembled to form the square depicted in
As depicted in
The novel shape-shifting surfaces may have intrinsic curvature such as spheres and use elements produced using planar fabrication techniques. Double layers of shape-shifting surfaces unit-cells of dissimilar size as depicted in
In this cube, there are eight (8) different sets of three identical compliant links or side members made to form the cube. Set one, depicted in
In
A shape-shifting surface may act as a physical barrier. For example, a shape-shifting surface used in biomedical applications may serve as a barrier against fluids. Thus, it may be important to evaluate barrier effectiveness as a function of the design parameters of the shape-shifting surface. The novel synthesis methodology subdivides the area covered by a unit cell and insures that overlaps prevent gaps in the surface from opening when the surface deforms. This is essentially a line-of-sight synthesis technique, and does not guarantee that the surface is a water-tight barrier. Labyrinth and diaphragm seals enhance the line-of-sight approach. Labyrinth seals make use of the friction in lengthy small passages to minimize and stop fluid flow. An elastomeric flexible membrane forms the barrier in diaphragm seals.
Surface integrity during a shape-shift depends on correct geometric and motion design in synergy with appropriate material choices. By including sensors that monitor the strength and nature of the loads on the surfaces, health monitoring, appropriate repair and, if necessary, redesign and replacement can be conducted to insure that surface integrity is maintained in the short and long term. The inclusion of actuators allows the surface to actively reshape or stiffen itself in order to respond to hazards that threaten the integrity of the surface. For example, with a shape-shifting surface implemented into extreme cold weather roofing systems, damage due to excess snow buildup can be prevented. Strain sensors in an innovative system can determine when the weight of the overlying snow is unsafe, and employ a shape-shift, such as a shrugging motion, to dislocate the snow from the roof while maintaining a physical barrier to keep the snow out of the roofed area.
Shape-shifting surfaces are compatible with finite element modeling. They can be used in the design of a specific planar shape-shift as well as in the design of out-of-plane curvature and flexibility.
It will thus be seen that the objects set forth above, and those made apparent from the foregoing disclosure, are efficiently attained. Since certain changes may be made in the above construction without departing from the scope of the invention, it is intended that all matters contained in the foregoing disclosure or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.
It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described, and all statements of the scope of the invention that, as a matter of language, might be said to fall therebetween.
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